How to have rigid-bodies and charge fields interact?
It would seem that there is a paradox going on in the (blender) physics...

from the manual

"Charge
It is similar to spherical field except it changes behavior (attract/repulse) based on the effected particles charge field (negative/positive), like real particles with a charge. This mean this field has only effect on particles that have also a Charge field (else, they have no “charge”, and hence are unaffected)!"

Unfortunately this means that charged objects will only affect other charged objects and that giving an object a charge (force/field), turns it into an effector, and therefore does not affect other effectors...

With the field added to an empty, the field will have no effect on the uncharged spheres.

Seems like a bug/glitch/oversight/unintended consequence of the negation of the effectors affecting each other.